Vehicles may be equipped with bumper assemblies and impact protection structures that elastically and plastically deform to absorb energy in the event of an impact. A number of standards and tests currently exist. Various organizations are introducing a number of pedestrian regulations and rating criteria for automotive vehicles. As one example, test methods have been developed to assess the protection of an adult pedestrian by simulating leg-impact conditions during a car-to-pedestrian impact. Generally, under such testing conditions, a bumper assembly with a bumper cover that is compliant in a direction of impact that is parallel to the ground will decrease a bending moment experienced by lower parts of the leg. However, in bumper assemblies constructed with bumper covers that are compliant in this direction, the bumper covers are often overly compliant in the vertical direction, which is undesirable. Accordingly, alternative bumper assemblies are desired.